Schools can get licenses for the Air Server mirroring software for just under four bucks per laptop. Apple TV is just under $100 each and Reflector runs around $13 per device. In my experience they all offer about the same level of service except that Apple TV can be reflected to a television. (This is unnecessary in schools with projectors.) Downloading and installing the Airserver software onto a laptop is quick and easy. From there, you are prompted to provide your activation code.
Once installed you can set private passwords and I recommend that you do. Once mischievous crumb snatchers know how to use the controls, they can co-opt your display with whatever happens to be on their iPad. A recipe for disaster to say the least. When you want the students to display their work, you have options to allow access. You can select to send them a password or passcode that is displayed on your desktop that they punch in or you can have them ask you. You can also select no Password but I would only do this if I completely trusted the class not to try it and lets face it, seeing your iPad up there in the front is pretty tempting.
One lesson we learned the hard way after installing Airserver on all the laptops at our school is that you need to have recognizable names for each laptop. Otherwise all the laptops on the wireless network will show up in the students iPad and they will not know which name to select when they go to turn on mirroring. I recommend a system based on the teacher's last name and subjects taught. (Of course this all depends on the size of your school and how many Mrs. Johnson's you have teaching there.)
Embedded into this blog is a tutorial for how to use Airserver for both teachers and students. If you would like to download it you can also find it here. http://midd.me/DTMr
Last but not least, at the time of publishing this post, iOS7 is still crashing when mirroring to any service after 2 or 3 minutes. If the iPad crashes it can be rebooted by holding the home button and the power button at the same time for ten seconds. To avoid crashing the iPad, keep the mirroring to less than two minutes. In the meantime, let your displeasure be known to Apple so that they fix the bug. http://www.apple.com/feedback/ipad.html